So this specific user is getting some site emails or none at all?
Are you self hosted?
If so, and this is user specific and affects all their emails, have you checked it’s not being suppressed by your mail service? Often, if the mail has ever bounced, even once, it can automatically be added to your suppressed list. From then on it will never be sent. This mechanism helps avoid the mail service getting a bad rep and harming its general delivery capability.
Check your mail service logs, the suppressed list and contact their support if necessary. You may be able to remove it from the suppressed list.
You may be able to set their password manually as a one-off using the rails console but this is not good practice of course (especially if they have no way of then resetting themselves again) and you should really address the underlying mail issue because so much relies on the email delivery in Discourse.